𝐼𝑃_𝑟-sets, Szemerédi’s theorem, and Ramsey theory

Furstenberg, H.; Katznelson, Y.

doi:10.1090/S0273-0979-1986-15438-8

Bulletin of the American Mathematical Society

The Bulletin publishes expository articles on contemporary mathematical research, written in a way that gives insight to mathematicians who may not be experts in the particular topic. The Bulletin also publishes reviews of selected books in mathematics and short articles in the Mathematical Perspectives section, both by invitation only.

ISSN 1088-9485 (online) ISSN 0273-0979 (print)

The 2020 MCQ for Bulletin of the American Mathematical Society is 0.84.

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$IP{\textunderscore }r$-sets, Szemerédi’s theorem, and Ramsey theory
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by H. Furstenberg and Y. Katznelson PDF

Bull. Amer. Math. Soc. 14 (1986), 275-278

References

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H. Furstenberg, Recurrence in ergodic theory and combinatorial number theory, Princeton University Press, Princeton, N.J., 1981. M. B. Porter Lectures. MR 603625, DOI 10.1515/9781400855162
H. Furstenberg and Y. Katznelson, An ergodic Szemerédi theorem for IP-systems and combinatorial theory, J. Analyse Math. 45 (1985), 117–168. MR 833409, DOI 10.1007/BF02792547
Ronald L. Graham, Bruce L. Rothschild, and Joel H. Spencer, Ramsey theory, Wiley-Interscience Series in Discrete Mathematics, John Wiley & Sons, Inc., New York, 1980. MR 591457